Let X be a random variable that represents the percentage of time a computer processor is active in any day. The cumulative density function (CDF) of X is given by FX(x) = K(x2 + 3x); 0 x 1 where K is a constant. (a) What is the value of K? (b) Determine the probability density function (PDF) of X. (c) Calculate the average percentage of time the processor is idle? (d) Let Y be a random variable that represents the percentage of time an external memory is accessed from the computer in any day. Y is modeled as Y = 2X -1. Determine the average percentage of time the memory is accessed. (e) Calculate the variance of Y .